### Some(?) of the Parts

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle

### Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

### At a Glance

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

# Nicely Similar

##### Stage: 4 Challenge Level:

Well done to the people who found the height (48) and then used it to get the triangle side lengths, but special congratulations to Michael from Taradale High School for a more direct approach using the powerful property that this arrangement contains three similar triangles.

If the yellow triangle has a hypotenuse, h, and if the yellow-orange triangle and the yellow triangle are similar, then the ratio, h : 100 is equal to the ratio 36 : h

From that we know that h must be 60, and using the same thinking again the hypotenuse of the orange triangle must be 80.